The definition of the N-ary reflected Gray code is given. Two recursive algorithms for generating the N-ary reflected Gray codes are presented: one algorithm is coded directly from the definition; another algorithm is derived from the sequencing orders of digits in the N-ary reflected Gray codes. It is shown that these two algorithms are equivalent functionally. Furthermore, it is proven that the N-ary reflected Gray code is cyclic when its radix is even, but not cyclic, in general, when its radix is odd.